Buy and read Healthy Sleep Habits, Happy Child by Dr. Marc Weissbluth. While he is a local pediatrician who specializes in infant/child sleep issues, he is nationally known and recognized for his decades of work and expertise in the area of sleep.
His methods involve allowing the child to cry it out, either through extinction (put them to sleep and that's it) or gradual extinction (put them to sleep, check back every few minutes). If this doesn't merge with your parenting philosophies, then skip it entirely. Her pattern at home has been "I go to sleep with mommy's help, every night all the time". You're asking her to change that habit. She's not going to give it up willingly and without some resistance. Whatever 'change technique' you choose to use, you have to do two things: #1) understand that she could need a week or two to get used to the new routines and #2) be painstakingly consistent, which means if you are going to commit to a method you cannot revert back to the old ways if you *truly* want them to change. Being inconsistent only leads to her confusion - "wait, two nights ago they made me cry but last night when I cried they came and rocked me, so tonight here I am crying again and they aren't coming to get me so it is time to cry and scream louder until they come running".
Since you indicate that she doesn't have problems sleeping at daycare (I'm going to guess they put ALL the kids down at the same time and don't rock/hold/whatever), she is perfectly capable of sleeping at home.